Scheduling to minimize max flow time: Off-line and on-line algorithms

We investigate the max flow time scheduling problem in the off-line and on-line setting. We prove positive and negative theoretical results. In the off-line setting, we address the unrelated parallel machines model and present the first known fully polynomial time approximation scheme, when the number of machines is fixed. In the on-line setting and when the machines are identical, we analyze the First In First Out (FIFO) heuristic when preemption is allowed. We show that FIFO is an on-line algorithm with a 3−2/m-competitive ratio. Finally, we present two lower bounds on the competitive ratio of deterministic on-line algorithms.